Translation Equivariant Transformer Neural Processes (2406.12409v1)

Abstract: The effectiveness of neural processes (NPs) in modelling posterior prediction maps -- the mapping from data to posterior predictive distributions -- has significantly improved since their inception. This improvement can be attributed to two principal factors: (1) advancements in the architecture of permutation invariant set functions, which are intrinsic to all NPs; and (2) leveraging symmetries present in the true posterior predictive map, which are problem dependent. Transformers are a notable development in permutation invariant set functions, and their utility within NPs has been demonstrated through the family of models we refer to as TNPs. Despite significant interest in TNPs, little attention has been given to incorporating symmetries. Notably, the posterior prediction maps for data that are stationary -- a common assumption in spatio-temporal modelling -- exhibit translation equivariance. In this paper, we introduce of a new family of translation equivariant TNPs that incorporate translation equivariance. Through an extensive range of experiments on synthetic and real-world spatio-temporal data, we demonstrate the effectiveness of TE-TNPs relative to their non-translation-equivariant counterparts and other NP baselines.

• The paper presents translation equivariant attention mechanisms that ensure spatial and temporal consistency in neural processes.
• It incorporates a pseudo-token approach to reduce quadratic complexity, enabling efficient handling of large spatio-temporal datasets.
• Empirical results on synthetic and real-world data validate superior generalisation and performance over traditional models.

Translation Equivariant Transformer Neural Processes

The paper "Translation Equivariant Transformer Neural Processes" introduces a novel family of models termed Translation Equivariant Transformer Neural Processes (TE-TNPs). These models extend the framework of Transformer Neural Processes (TNPs), incorporating translation equivariance to enhance their proficiency in handling spatio-temporal data. This enhancement is particularly crucial for tasks where the data exhibits stationary characteristics, typical of many real-world spatio-temporal datasets.

Background and Motivation

Neural Processes (NPs) have been instrumental in modelling posterior predictive distributions, with significant advancements attributed to the improvements in permutation invariant set functions and the incorporation of symmetries derived from the modelling context. Transformers, being potent permutation invariant set functions, have been integral in advancing NP architectures, giving rise to the TNP family. However, prior TNP variants have largely overlooked the integration of symmetries, specifically translation equivariance, crucial for datasets assuming stationarity in spatio-temporal domains.

Contributions

The proposed TE-TNP models incorporate translation equivariance directly at the architectural level. This is achieved by replacing the standard attention mechanisms in transformers with newly developed translation equivariant multi-head self-attention (TE-MHSA) and translation equivariant multi-head cross-attention (TE-MHCA) operations. The main contributions of the paper are as follows:

1. Translation Equivariant Attention Mechanisms: The authors develop TE-MHSA and TE-MHCA, allowing the attention operations to respect translation symmetries inherently present in stationary processes. These operations ensure that if data points are translated spatially or temporally, the predictions are translated correspondingly, maintaining the integrity of the model outputs.
2. Computational Efficiency via Pseudo-Tokens: To manage the computational complexity associated with large datasets, the authors introduce a pseudo-token based approach, leading to Translation Equivariant Pseudo-Token Transformer Neural Processes (TE-PT-TNPs). This innovation reduces the quadratic complexity typical of conventional attention mechanisms to a more manageable scale.
3. Empirical Validation: Through comprehensive experiments on both synthetic and real-world datasets, including challenging environmental and fluid dynamics datasets, TE-TNPs and their pseudo-token variants demonstrate superior performance over traditional TNPs and other NP baselines.

Theoretical Insights

The paper provides strong theoretical underpinnings for the benefits of translation equivariance, particularly in enhancing spatial generalisation. The authors prove that translation equivariance in the model's architecture can significantly improve generalisation performance when the underlying data generation process is indeed stationary. This theoretical insight is supported by experimental evidence where TE-TNPs outperform other models when applied to shifted or translated datasets, underscoring the practical utility of the proposed mechanisms.

Implications and Future Work

The implications of this research are multifaceted:

• Practical Applications: In domains such as climate modelling, environmental science, and dynamic systems where data naturally manifests translation equivariance, TE-TNPs offer a robust modelling framework.
• Theoretical Extensions: The formal treatment of equivariance in transformer-based architectures opens pathways for extending these principles to other forms of symmetry, potentially integrating them with broader classes of geometric and group-theoretic models.

Looking forward, the exploration of additional pseudo-token architectures and further optimisation of the translation equivariant attention mechanisms could enhance both the scalability and efficiency of these models. Moreover, integrating these concepts with emerging technologies like large-scale sequence models could yield even richer insights and applications.

In conclusion, the translation equivariant enhancements to TNPs position these models at the forefront of spatio-temporal learning tasks, providing a robust mechanism to leverage inherent data symmetries effectively. This work not only contributes new tools but also sets a compelling agenda for future research in machine learning architectures sensitive to domain-specific symmetries.